Finite-element-method expectation values for correlated two-electron wave functions

Journal Article · Fri Sep 01 04:00:00 EDT 1995 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.52.1968· OSTI ID:115902

Ackermann, J ^[1]

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1. Institut fuer Molekulare Biotechnologie (IMB), Beutenbergstrasse 11, D-07745 Jena (Germany)

The Schroedinger equation for the ground state of correlated two-electron atoms is treated by an accurate finite-element method (FEM) yielding energy eigenvalues of {minus}2.903 724 377 021 a.u. for the helium atom and {minus}0.527 751 016 532 a.u. for the hydrogen ion H{sup {minus}}. By means of an adaptive multilevel grid refinement the FEM energy eigenvalue is improved to a precision of 1{times}10{sup {minus}11} a.u., which is comparable to results obtained with sophisticated global basis sets. The local and overall precision of the FEM wave function approximation is studied and discussed. Benchmark values for the expectation values {l_angle}{ital r}{sup 2}{r_angle}, {l_angle}{ital r}{r_angle}, {l_angle}1/{ital r}{r_angle}, and {l_angle}1/{ital r}{sub 12}{r_angle} are presented.

• OSTI ID: 115902
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 3 Vol. 52; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ELECTRON CORRELATION
EXPECTATION VALUE
FINITE ELEMENT METHOD
GROUND STATES
HELIUM
HYDROGEN IONS 1 MINUS
WAVE FUNCTIONS